Summary: High and Low Temperature Series Estimates for the Critical
Temperature of the 3D Ising Model
Zaher Salman and Joan Adler
Department of Physics, Technion­Israel Institute of Technology,
Haifa 32000, Israel
Abstract
We have analysed low and high temperature series expansions for the
three­dimensional Ising model on the simple cubic lattice. Our analysis
of Butera and Comi's new 32 term high temperature series yields K c =
0:221659\Sigma +0:000002
\Gamma0:000005 and from the 32 term low temperature series of Vohwinkel
we find K c = 0:22167 \Sigma 0:00002, consistent with the high temperature series
but with larger error bars. We discuss the reasons for the larger error bars on
the low temperature side and compare these values with estimates from other
series analyses and from simulations.
I. INTRODUCTION
The critical temperature of the three­dimensional (3d) Ising model on the simple cubic
lattice has been exhaustively studied by many authors with many methods. The reason for
this concentrated effort is very simple ­ the 3d Ising model is one of the simplest models
of three­dimensional phase transitions with some of the best experimental data from real